Elements Of Differentiable Dynamics And Bifurcation Theory
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Elements Of Differentiable Dynamics And Bifurcation Theory
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Author : David Ruelle
language : en
Publisher: Elsevier
Release Date : 2014-05-10
Elements Of Differentiable Dynamics And Bifurcation Theory written by David Ruelle and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Elements of Differentiable Dynamics and Bifurcation Theory provides an introduction to differentiable dynamics, with emphasis on bifurcation theory and hyperbolicity that is essential for the understanding of complicated time evolutions occurring in nature. This book discusses the differentiable dynamics, vector fields, fixed points and periodic orbits, and stable and unstable manifolds. The bifurcations of fixed points of a map and periodic orbits, case of semiflows, and saddle-node and Hopf bifurcation are also elaborated. This text likewise covers the persistence of normally hyperbolic manifolds, hyperbolic sets, homoclinic and heteroclinic intersections, and global bifurcations. This publication is suitable for mathematicians and mathematically inclined students of the natural sciences.
Elements Of Applied Bifurcation Theory
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Author : Yuri Kuznetsov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Elements Of Applied Bifurcation Theory written by Yuri Kuznetsov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Providing readers with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems, the focus here is on efficient numerical implementations of the developed techniques. The book is designed for advanced undergraduates or graduates in applied mathematics, as well as for Ph.D. students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used. This new edition preserves the structure of the first while updating the context to incorporate recent theoretical developments, in particular new and improved numerical methods for bifurcation analysis.
Bifurcation Theory Of Impulsive Dynamical Systems
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Author : Kevin E.M. Church
language : en
Publisher: Springer Nature
Release Date : 2021-03-24
Bifurcation Theory Of Impulsive Dynamical Systems written by Kevin E.M. Church and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-24 with Mathematics categories.
This monograph presents the most recent progress in bifurcation theory of impulsive dynamical systems with time delays and other functional dependence. It covers not only smooth local bifurcations, but also some non-smooth bifurcation phenomena that are unique to impulsive dynamical systems. The monograph is split into four distinct parts, independently addressing both finite and infinite-dimensional dynamical systems before discussing their applications. The primary contributions are a rigorous nonautonomous dynamical systems framework and analysis of nonlinear systems, stability, and invariant manifold theory. Special attention is paid to the centre manifold and associated reduction principle, as these are essential to the local bifurcation theory. Specifying to periodic systems, the Floquet theory is extended to impulsive functional differential equations, and this permits an exploration of the impulsive analogues of saddle-node, transcritical, pitchfork and Hopf bifurcations. Readers will learn how techniques of classical bifurcation theory extend to impulsive functional differential equations and, as a special case, impulsive differential equations without delays. They will learn about stability for fixed points, periodic orbits and complete bounded trajectories, and how the linearization of the dynamical system allows for a suitable definition of hyperbolicity. They will see how to complete a centre manifold reduction and analyze a bifurcation at a nonhyperbolic steady state.
Fundamentals Of Dynamical Systems And Bifurcation Theory
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Author : Milan Medved̕
language : en
Publisher: CRC Press
Release Date : 1992-05-21
Fundamentals Of Dynamical Systems And Bifurcation Theory written by Milan Medved̕ and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-05-21 with Mathematics categories.
This graduate level text explains the fundamentals of the theory of dynamical systems. After reading it you will have a good enough understanding of the area to study the extensive literature on dynamical systems. The book is self contained, as all the essential definitions and proofs are supplied, as are useful references: all the reader needs is a knowledge of basic mathematical analysis, algebra and topology. However, the first chapter contains an explanation of some of the methods of differential topology an understanding of which is essential to the theory of dynamical systems. A clear introduction to the field, which is equally useful for postgraduates in the natural sciences, engineering and economics.
Bifurcations And Chaos In Piecewise Smooth Dynamical Systems
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Author : Zhanybai T. Zhusubaliyev
language : en
Publisher: World Scientific
Release Date : 2003
Bifurcations And Chaos In Piecewise Smooth Dynamical Systems written by Zhanybai T. Zhusubaliyev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Technical problems often lead to differential equations withpiecewise-smooth right-hand sides. Problems in mechanicalengineering, for instance, violate the requirements of smoothness ifthey involve collisions, finite clearances, or stickOCoslipphenomena."
Bifurcation In Autonomous And Nonautonomous Differential Equations With Discontinuities
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Author : Marat Akhmet
language : en
Publisher: Springer
Release Date : 2017-01-23
Bifurcation In Autonomous And Nonautonomous Differential Equations With Discontinuities written by Marat Akhmet and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-23 with Mathematics categories.
This book focuses on bifurcation theory for autonomous and nonautonomous differential equations with discontinuities of different types – those with jumps present either in the right-hand side, or in trajectories or in the arguments of solutions of equations. The results obtained can be applied to various fields, such as neural networks, brain dynamics, mechanical systems, weather phenomena and population dynamics. Developing bifurcation theory for various types of differential equations, the book is pioneering in the field. It presents the latest results and provides a practical guide to applying the theory to differential equations with various types of discontinuity. Moreover, it offers new ways to analyze nonautonomous bifurcation scenarios in these equations. As such, it shows undergraduate and graduate students how bifurcation theory can be developed not only for discrete and continuous systems, but also for those that combine these systems in very different ways. At the same time, it offers specialists several powerful instruments developed for the theory of discontinuous dynamical systems with variable moments of impact, differential equations with piecewise constant arguments of generalized type and Filippov systems.
Elements Of Applied Bifurcation Theory
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Author : Yuri A. Kuznetsov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Elements Of Applied Bifurcation Theory written by Yuri A. Kuznetsov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
A solid basis for anyone studying the dynamical systems theory, providing the necessary understanding of the approaches, methods, results and terminology used in the modern applied-mathematics literature. Covering the basic topics in the field, the text can be used in a course on nonlinear dynamical systems or system theory. Special attention is given to efficient numerical implementations of the developed techniques, illustrated by several examples from recent research papers. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used, making this book suitable for advanced undergraduate or graduate students in applied mathematics, as well as for researchers in other disciplines who use dynamical systems as model tools in their studies.
Bifurcation Theory And Methods Of Dynamical Systems
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Author : Dingjun Luo
language : en
Publisher: World Scientific
Release Date : 1997
Bifurcation Theory And Methods Of Dynamical Systems written by Dingjun Luo and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Science categories.
Dynamical bifurcation theory is concerned with the changes that occur in the global structure of dynamical systems as parameters are varied. This book makes recent research in bifurcation theory of dynamical systems accessible to researchers interested in this subject. In particular, the relevant results obtained by Chinese mathematicians are introduced as well as some of the works of the authors which may not be widely known. The focus is on the analytic approach to the theory and methods of bifurcations. The book prepares graduate students for further study in this area, and it serves as a ready reference for researchers in nonlinear sciences and applied mathematics.
Essential Elements Of Nonlinearity Bifurcation And Chaos Theory
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Author : Frank Scott
language : en
Publisher: States Academic Press
Release Date : 2021-11-16
Essential Elements Of Nonlinearity Bifurcation And Chaos Theory written by Frank Scott and has been published by States Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-16 with Mathematics categories.
The three common features exhibited by both natural and technological processes are nonlinearity, bifurcation and chaos theory. Floquet exponents and bifurcations in switched converters, dynamics of a pendulum of variable length, mathematical modeling, and non-linearity in structural dynamics are some of the significant concepts in this area of study. The mathematical study of changes in the qualitative structure of a given family and solutions of family of differential equations is referred as bifurcation theory. The branch of mathematics which deals with the study of chaos in dynamical systems where the irregularities and random states of disorder are governed by underlying patterns and deterministic laws is termed as chaos theory. The book presents researches and studies performed by experts across the globe. It includes some of the vital pieces of work being conducted across the world, on various topics related to essential elements of nonlinearity, bifurcation and chaos theory. This book is a resource guide for experts as well as students.
Bifurcation Theory Of Functional Differential Equations
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Author : Shangjiang Guo
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-30
Bifurcation Theory Of Functional Differential Equations written by Shangjiang Guo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-30 with Mathematics categories.
This book provides a crash course on various methods from the bifurcation theory of Functional Differential Equations (FDEs). FDEs arise very naturally in economics, life sciences and engineering and the study of FDEs has been a major source of inspiration for advancement in nonlinear analysis and infinite dimensional dynamical systems. The book summarizes some practical and general approaches and frameworks for the investigation of bifurcation phenomena of FDEs depending on parameters with chap. This well illustrated book aims to be self contained so the readers will find in this book all relevant materials in bifurcation, dynamical systems with symmetry, functional differential equations, normal forms and center manifold reduction. This material was used in graduate courses on functional differential equations at Hunan University (China) and York University (Canada).